Input output tables
•
1 like•1,085 views
The document discusses functions in mathematics and provides examples of evaluating different functions based on input-output tables: 1) It introduces functions in real life and mathematics, and provides the example function y=x+3, showing how to fill out an input-output table for it. 2) More examples of functions are given as practice problems for the reader to fill out tables for, including y=x-4 and y=-3x. 3) An input-output table is shown for the function y=2x+3 to evaluate. 4) A more difficult function is presented as y=x/-3, with an empty table for the reader to solve. 5)
Report
Share
Report
Share
Download to read offline
Recommended
Expresiones algebraicas
The document discusses algebraic expressions including:
- Adding, subtracting, and finding the numerical value of expressions
- Factorizing expressions using the product of sums/differences and factoring trinomials
- Simplifying fractions through factoring the numerator and denominator
- Performing operations like multiplication, division, addition and subtraction on fractions
It also covers factorizing algebraic expressions using Ruffini's method.
Ecuaciones
The document contains examples of simple first-degree equations with:
- No parentheses or denominators
- Terms grouped together
- Parentheses
The equations are solved for the variable x, with the solutions provided.
Tugas matik ii
The document provides examples of factorizing quadratic equations and completing the square to solve quadratic equations. It discusses:
1) Factoring quadratic expressions like x2 + 5x - 50, x2 + 3x, and 2x2 + 3x + 1.
2) Completing the square to solve equations like x2 + 5x + 4 = 0 and 2x2 - 14x + 12 = 0.
3) Using the quadratic formula to solve equations like x2 - 15x + 30 = 0, x2 + 8x - 20 = 0, and x2 + 3x = 0.
4) Setting the discriminant equal to 0 to find the value of p that makes the equation
Stefan Kanev: Clojure, ClojureScript and Why They're Awesome at I T.A.K.E. Un...
This document summarizes a presentation about Clojure and ClojureScript. It describes Clojure as a modern Lisp dialect that runs on the JVM with a focus on concurrency. It notes advantages like stable platforms, access to Java libraries, and immutable persistent data structures that facilitate parallelism. The document discusses Clojure concepts like homoiconicity, concurrency vs parallelism, syntax using s-expressions, macros for metaprogramming, and data structures like maps, vectors, and sets. It also mentions ClojureScript and domain-specific languages.
1 4 homework
This document contains examples of multiplying, expanding, and simplifying rational expressions. Some examples involve breaking rational expressions into sums and differences of fractions. Other examples use long division to write rational expressions in the form of a quotient plus a remainder over the divisor. The rational expressions involve variables and operations.
ゲーム理論BASIC 第40回 -仁-
The document presents information about submodular functions including:
1) It defines a submodular function v as a set function whose domain is the power set of a ground set N, and discusses properties of submodular functions.
2) It provides an example of a submodular function v with ground set N={1,2,3} and defines the polyhedron and base polyhedron associated with v.
3) It introduces the concept of a greedy algorithm for maximizing a submodular set function and outlines the steps of the greedy algorithm.
F12 2 -ans
1) The document contains 11 math word problems involving calculations with integers, variables, equations, and inequalities.
2) The problems cover topics like evaluating expressions, combining like terms, solving equations, and word problems about costs and sharing money.
3) The full solutions are shown for each problem.
ゲーム理論BASIC 第39回 -交渉集合とカーネル-
1) The document describes concepts and algorithms related to cooperative game theory and stable matchings. It presents definitions for cooperative games, the core of a game, and the stable matching problem.
2) Methods are introduced for finding solutions in the core for cooperative games and stable matchings for the stable matching problem using algorithms that assign values and make comparisons between players/options.
3) The document provides mathematical notation and context to formally define key concepts like cooperative games, the core, stable matchings, and algorithms for finding stable solutions.
Recommended
Expresiones algebraicas
The document discusses algebraic expressions including:
- Adding, subtracting, and finding the numerical value of expressions
- Factorizing expressions using the product of sums/differences and factoring trinomials
- Simplifying fractions through factoring the numerator and denominator
- Performing operations like multiplication, division, addition and subtraction on fractions
It also covers factorizing algebraic expressions using Ruffini's method.
Ecuaciones
The document contains examples of simple first-degree equations with:
- No parentheses or denominators
- Terms grouped together
- Parentheses
The equations are solved for the variable x, with the solutions provided.
Tugas matik ii
The document provides examples of factorizing quadratic equations and completing the square to solve quadratic equations. It discusses:
1) Factoring quadratic expressions like x2 + 5x - 50, x2 + 3x, and 2x2 + 3x + 1.
2) Completing the square to solve equations like x2 + 5x + 4 = 0 and 2x2 - 14x + 12 = 0.
3) Using the quadratic formula to solve equations like x2 - 15x + 30 = 0, x2 + 8x - 20 = 0, and x2 + 3x = 0.
4) Setting the discriminant equal to 0 to find the value of p that makes the equation
Stefan Kanev: Clojure, ClojureScript and Why They're Awesome at I T.A.K.E. Un...
This document summarizes a presentation about Clojure and ClojureScript. It describes Clojure as a modern Lisp dialect that runs on the JVM with a focus on concurrency. It notes advantages like stable platforms, access to Java libraries, and immutable persistent data structures that facilitate parallelism. The document discusses Clojure concepts like homoiconicity, concurrency vs parallelism, syntax using s-expressions, macros for metaprogramming, and data structures like maps, vectors, and sets. It also mentions ClojureScript and domain-specific languages.
1 4 homework
This document contains examples of multiplying, expanding, and simplifying rational expressions. Some examples involve breaking rational expressions into sums and differences of fractions. Other examples use long division to write rational expressions in the form of a quotient plus a remainder over the divisor. The rational expressions involve variables and operations.
ゲーム理論BASIC 第40回 -仁-
The document presents information about submodular functions including:
1) It defines a submodular function v as a set function whose domain is the power set of a ground set N, and discusses properties of submodular functions.
2) It provides an example of a submodular function v with ground set N={1,2,3} and defines the polyhedron and base polyhedron associated with v.
3) It introduces the concept of a greedy algorithm for maximizing a submodular set function and outlines the steps of the greedy algorithm.
F12 2 -ans
1) The document contains 11 math word problems involving calculations with integers, variables, equations, and inequalities.
2) The problems cover topics like evaluating expressions, combining like terms, solving equations, and word problems about costs and sharing money.
3) The full solutions are shown for each problem.
ゲーム理論BASIC 第39回 -交渉集合とカーネル-
1) The document describes concepts and algorithms related to cooperative game theory and stable matchings. It presents definitions for cooperative games, the core of a game, and the stable matching problem.
2) Methods are introduced for finding solutions in the core for cooperative games and stable matchings for the stable matching problem using algorithms that assign values and make comparisons between players/options.
3) The document provides mathematical notation and context to formally define key concepts like cooperative games, the core, stable matchings, and algorithms for finding stable solutions.
ゲーム理論BASIC 第36回 -続・交渉集合-
The document presents an optimization problem involving sets N and v. It defines the sets A(v), B(v), and C(v) which are related to feasible and optimal solutions. It gives an example where N = {1,2,3}, v assigns values to various subsets of N, and C(v) contains the single optimal solution (10,0,0). It then discusses using epsilon perturbations to solutions to show that other solutions are not optimal.
Ecs lineales
This document contains 26 equations to solve for the variable x. The equations involve adding, subtracting, multiplying and dividing terms with x. Students are instructed to copy the equations into their notebook and solve for x in each case. The solutions provided range from simple integers to more complex fractional values of x.
ゲーム理論BASIC 第37回 -カーネル-
1) The document defines a set N and a valuation function v that assigns values to subsets of N. It defines an allocation as a vector x in the set A(v).
2) It introduces several notation for different concepts: e(S,x) as the excess of set S under allocation x, Tij as the sets relevant to compare i and j, sij(x) as the strength of preference of i over j under x.
3) It provides an example where N={1,2,3}, v assigns a value of 10 to some pairs but 0 to others, and the core allocation C(v) consists of the vector (10,0,0).
Expresiones algebraicas carlet
The document discusses various algebraic expressions and methods for manipulating them. It covers topics like:
- Adding, subtracting, and evaluating algebraic expressions
- Factorizing expressions using product of binomials and the difference of squares
- Simplifying fractions by factorizing the numerator and denominator
- Performing operations like addition, subtraction, multiplication, and division on algebraic fractions
- Using the Ruffini method to factorize expressions and solve equations
The document provides examples and step-by-step workings for each of these algebraic techniques.
drill
everyday drill :)
one way to improve the mastery of the students is to have a 5 - minute drill before the lesson starts. "make it a habit"
#practicePamore
Multiplying Polynomials
1) The document discusses multiplying different types of polynomials, including: monomials, binomials, and polynomials with more than two terms.
2) It provides examples and steps for multiplying a monomial by a monomial, monomial by a polynomial, binomial by binomial, and a polynomial by a polynomial with three or more terms.
3) The key steps are distributing terms, applying rules like the distributive property, and combining like terms in the results.
ゲーム理論BASIC 第32回 -市場ゲームとコア-
The document describes an optimization problem and its solution. It defines a set N, weights wi for each element i in N, and utility functions ui for each i. It defines a function v(S) that finds the maximum utility for a subset S of N, subject to capacity constraints based on the weights. It then describes the optimal solution (p*,{x*i}) that maximizes total utility minus costs, with x*i defined for each i.
Alg lesson 11
The document provides notes and practice problems on multiplying and dividing real numbers. It covers the following key points:
1) Multiplying a positive number by -1 results in a negative number, and multiplying any number by 0 equals 0.
2) Numbers can be positive or negative, and the sign of the result of multiplication or division depends on whether the signs of the numbers are the same or different.
3) Worked examples are provided to demonstrate multiplying, dividing, and evaluating expressions involving positive and negative real numbers.
Two step equations quiz-practice
This document contains 6 two-step equations to solve using the inverse operations (symbolic) method. The equations involve variables such as x, and operations such as addition, subtraction, multiplication and division. The goal is to isolate the variable on one side of the equal sign by performing the inverse operation of the other side.
Algebra 7 Point 3
1) The document discusses factoring trinomials of the form x^2 + bx + c by using the FOIL method in reverse.
2) It provides examples of factoring trinomials with positive and negative signs using FOIL, and introduces a sign flowchart to determine the signs of the binomial factors.
3) The key steps are to write the trinomial as a product of two binomials, look at the signs to determine the signs in the binomial factors, then guess and check the last two numbers to fully factor the trinomial.
Ejercicios de verano para primero de eso
The document contains 74 math word problems with solutions of the form x=n. The problems involve solving linear equations for variable x and range in complexity from single variable equations to multi-step equations with fractions and variables on both sides. The solutions provided indicate the value of x that satisfies each equation.
V. Dragovic: Geometrization and Generalization of the Kowalevski top
This document summarizes the contents of a presentation on geometry and integrability. It discusses topics like Sophie Kowalevski's work, billiards within ellipses, the Poncelet theorem, generalizations of the Darboux theorem, the Kowalevski top, and discriminantly separable polynomials. It also presents theorems regarding properties of billiard trajectories within ellipsoids and the geometric interpretation of the Kowalevski fundamental equation.
Day 3a subtracting integers day 2
This document provides instruction on subtracting integers. It includes examples to evaluate, such as finding the temperature difference between the record high and low in North Carolina. The document also provides homework assignments from pages 148-149 involving adding, subtracting, and evaluating integers. It concludes by asking how a student would explain the lesson on subtracting integers to an absent student.
3a. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.1)
Pedagogy of Mathematics (Part II) - Algebra, Algebra, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, Polynomials, Constants, variables, algebraic expression
Ky-thuat-bien-doi-vi-phan-de-tim-nguyen-ham
The document provides examples for calculating derivatives and integrals of functions. It begins by defining the derivative and introducing notation. Several properties of derivatives are then listed, followed by common derivative formulas. The remainder of the document consists of 8 examples solving integrals using the properties of derivatives and integral formulas. Each example shows the steps to calculate the integral of a given function.
Productos notables
This document provides formulas for expanding binomial squares and cubes as well as formulas for difference and sum of cubes. It then provides 10 practice problems applying these formulas, such as finding expressions given information about variables, simplifying expressions, and expanding and reducing binomial expressions.
Mathematica6
The document provides instructions for using Mathematica 6.0 to create direction field plots. It explains how to access Mathematica 6.0 from ITaP machines, how notebooks work in Mathematica, and provides the commands to generate a direction field plot for the differential equation y=x^2-1 between x=-3 and x=3. An example output of these commands in a Mathematica notebook is also shown.
0304 ch 3 day 4
The document provides step-by-step work to find the exact zeros of the polynomial function f(x) = 2x^5 - x^4 - 10x^3 + 5x^2 + 12x - 6. It begins by graphing the function to suggest a zero of 0.5 and then uses synthetic division to reduce the polynomial degree. This yields a quadratic function that is then factored to find the zeros of x = ±3 and x = ±2. The final zeros listed are 0.5, ±3, and ±2.
Adding and Subtracting Polynomials
The document contains 10 math word problems involving adding, subtracting, and simplifying polynomial expressions. The problems ask the student to perform operations on expressions with variables and simplify the results.
Alg1 8.3 Linear Combination
This document covers the topic of linear combination in algebra lessons. It explains that linear combination is the process of solving a system of linear equations by eliminating a variable through addition or subtraction of the equations. It provides examples of solving systems of linear equations using this elimination or addition-and-subtraction method. It also includes practice problems for students to try applying linear combination.
Pre-Alg 7.6 Triangles
This document provides a lesson on triangles that includes:
1) A review of the types of angles (acute, right, obtuse) and that in any triangle the sum of the interior angles is 180 degrees.
2) Examples of how to find the measure of an unknown angle using the 180 degree rule.
3) Practice problems identifying the type of triangle based on the angles and classifying sample triangles.
More Related Content
What's hot
ゲーム理論BASIC 第36回 -続・交渉集合-
The document presents an optimization problem involving sets N and v. It defines the sets A(v), B(v), and C(v) which are related to feasible and optimal solutions. It gives an example where N = {1,2,3}, v assigns values to various subsets of N, and C(v) contains the single optimal solution (10,0,0). It then discusses using epsilon perturbations to solutions to show that other solutions are not optimal.
Ecs lineales
This document contains 26 equations to solve for the variable x. The equations involve adding, subtracting, multiplying and dividing terms with x. Students are instructed to copy the equations into their notebook and solve for x in each case. The solutions provided range from simple integers to more complex fractional values of x.
ゲーム理論BASIC 第37回 -カーネル-
1) The document defines a set N and a valuation function v that assigns values to subsets of N. It defines an allocation as a vector x in the set A(v).
2) It introduces several notation for different concepts: e(S,x) as the excess of set S under allocation x, Tij as the sets relevant to compare i and j, sij(x) as the strength of preference of i over j under x.
3) It provides an example where N={1,2,3}, v assigns a value of 10 to some pairs but 0 to others, and the core allocation C(v) consists of the vector (10,0,0).
Expresiones algebraicas carlet
The document discusses various algebraic expressions and methods for manipulating them. It covers topics like:
- Adding, subtracting, and evaluating algebraic expressions
- Factorizing expressions using product of binomials and the difference of squares
- Simplifying fractions by factorizing the numerator and denominator
- Performing operations like addition, subtraction, multiplication, and division on algebraic fractions
- Using the Ruffini method to factorize expressions and solve equations
The document provides examples and step-by-step workings for each of these algebraic techniques.
drill
everyday drill :)
one way to improve the mastery of the students is to have a 5 - minute drill before the lesson starts. "make it a habit"
#practicePamore
Multiplying Polynomials
1) The document discusses multiplying different types of polynomials, including: monomials, binomials, and polynomials with more than two terms.
2) It provides examples and steps for multiplying a monomial by a monomial, monomial by a polynomial, binomial by binomial, and a polynomial by a polynomial with three or more terms.
3) The key steps are distributing terms, applying rules like the distributive property, and combining like terms in the results.
ゲーム理論BASIC 第32回 -市場ゲームとコア-
The document describes an optimization problem and its solution. It defines a set N, weights wi for each element i in N, and utility functions ui for each i. It defines a function v(S) that finds the maximum utility for a subset S of N, subject to capacity constraints based on the weights. It then describes the optimal solution (p*,{x*i}) that maximizes total utility minus costs, with x*i defined for each i.
Alg lesson 11
The document provides notes and practice problems on multiplying and dividing real numbers. It covers the following key points:
1) Multiplying a positive number by -1 results in a negative number, and multiplying any number by 0 equals 0.
2) Numbers can be positive or negative, and the sign of the result of multiplication or division depends on whether the signs of the numbers are the same or different.
3) Worked examples are provided to demonstrate multiplying, dividing, and evaluating expressions involving positive and negative real numbers.
Two step equations quiz-practice
This document contains 6 two-step equations to solve using the inverse operations (symbolic) method. The equations involve variables such as x, and operations such as addition, subtraction, multiplication and division. The goal is to isolate the variable on one side of the equal sign by performing the inverse operation of the other side.
Algebra 7 Point 3
1) The document discusses factoring trinomials of the form x^2 + bx + c by using the FOIL method in reverse.
2) It provides examples of factoring trinomials with positive and negative signs using FOIL, and introduces a sign flowchart to determine the signs of the binomial factors.
3) The key steps are to write the trinomial as a product of two binomials, look at the signs to determine the signs in the binomial factors, then guess and check the last two numbers to fully factor the trinomial.
Ejercicios de verano para primero de eso
The document contains 74 math word problems with solutions of the form x=n. The problems involve solving linear equations for variable x and range in complexity from single variable equations to multi-step equations with fractions and variables on both sides. The solutions provided indicate the value of x that satisfies each equation.
V. Dragovic: Geometrization and Generalization of the Kowalevski top
This document summarizes the contents of a presentation on geometry and integrability. It discusses topics like Sophie Kowalevski's work, billiards within ellipses, the Poncelet theorem, generalizations of the Darboux theorem, the Kowalevski top, and discriminantly separable polynomials. It also presents theorems regarding properties of billiard trajectories within ellipsoids and the geometric interpretation of the Kowalevski fundamental equation.
Day 3a subtracting integers day 2
This document provides instruction on subtracting integers. It includes examples to evaluate, such as finding the temperature difference between the record high and low in North Carolina. The document also provides homework assignments from pages 148-149 involving adding, subtracting, and evaluating integers. It concludes by asking how a student would explain the lesson on subtracting integers to an absent student.
3a. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.1)
Pedagogy of Mathematics (Part II) - Algebra, Algebra, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, Polynomials, Constants, variables, algebraic expression
Ky-thuat-bien-doi-vi-phan-de-tim-nguyen-ham
The document provides examples for calculating derivatives and integrals of functions. It begins by defining the derivative and introducing notation. Several properties of derivatives are then listed, followed by common derivative formulas. The remainder of the document consists of 8 examples solving integrals using the properties of derivatives and integral formulas. Each example shows the steps to calculate the integral of a given function.
Productos notables
This document provides formulas for expanding binomial squares and cubes as well as formulas for difference and sum of cubes. It then provides 10 practice problems applying these formulas, such as finding expressions given information about variables, simplifying expressions, and expanding and reducing binomial expressions.
Mathematica6
The document provides instructions for using Mathematica 6.0 to create direction field plots. It explains how to access Mathematica 6.0 from ITaP machines, how notebooks work in Mathematica, and provides the commands to generate a direction field plot for the differential equation y=x^2-1 between x=-3 and x=3. An example output of these commands in a Mathematica notebook is also shown.
0304 ch 3 day 4
The document provides step-by-step work to find the exact zeros of the polynomial function f(x) = 2x^5 - x^4 - 10x^3 + 5x^2 + 12x - 6. It begins by graphing the function to suggest a zero of 0.5 and then uses synthetic division to reduce the polynomial degree. This yields a quadratic function that is then factored to find the zeros of x = ±3 and x = ±2. The final zeros listed are 0.5, ±3, and ±2.
Adding and Subtracting Polynomials
The document contains 10 math word problems involving adding, subtracting, and simplifying polynomial expressions. The problems ask the student to perform operations on expressions with variables and simplify the results.
What's hot (20)
V. Dragovic: Geometrization and Generalization of the Kowalevski top
V. Dragovic: Geometrization and Generalization of the Kowalevski top
3a. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.1)
3a. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.1)
More from Jaqueline Vallejo
Alg1 8.3 Linear Combination
This document covers the topic of linear combination in algebra lessons. It explains that linear combination is the process of solving a system of linear equations by eliminating a variable through addition or subtraction of the equations. It provides examples of solving systems of linear equations using this elimination or addition-and-subtraction method. It also includes practice problems for students to try applying linear combination.
Pre-Alg 7.6 Triangles
This document provides a lesson on triangles that includes:
1) A review of the types of angles (acute, right, obtuse) and that in any triangle the sum of the interior angles is 180 degrees.
2) Examples of how to find the measure of an unknown angle using the 180 degree rule.
3) Practice problems identifying the type of triangle based on the angles and classifying sample triangles.
Alg1 8.2 Substitution Method
The document discusses the substitution method for solving systems of linear equations. It provides examples of using substitution to solve systems that have a unique solution, no solution, and infinitely many solutions. Step-by-step instructions are given for using substitution to isolate a variable and substitute it into the other equation to solve for the variables.
Alg1 7.13 Graphing Linear Inequalities
This document provides instructions for graphing linear inequalities on a coordinate plane. It reviews graphing linear equalities and defines the four types of inequalities: less than, greater than, less than or equal to, and greater than or equal to. Examples of individual inequalities are given, such as y > 5 and x ≤ 3. The document explains that the solution to an inequality includes all points on or within the boundary line. It poses questions about graphing an inequality line, including identifying the y-intercept, slope, border, shading, solutions and non-solutions.
Pre-Alg 6.7 Scientific Notation
This document provides an overview of scientific notation. It begins by reviewing positive and negative exponents. It then defines Avogadro's number as the number of molecules in a mole of a substance. It explains how to write numbers in scientific notation by moving the decimal point right if the power is positive or left if negative. Examples are given of converting between scientific and standard form. The document also demonstrates how to multiply numbers in scientific notation by keeping the numbers the same and adding the powers of ten.
Pre-Alg 7.2 Rays and Angles
This document provides an overview of angles and their definitions in geometry. It defines a ray as a line segment extending from an endpoint in one direction forever, and an angle as the figure formed by two rays sharing a common endpoint, called the vertex. Angles are classified as acute, right, or obtuse depending on whether they measure less than, equal to, or greater than 90 degrees. The document presents different naming conventions for angles based on identifying the vertex point or using numerical designations to avoid confusion when multiple angles share a vertex. It concludes by providing a link to an online game about identifying angles.
Pre-Alg 6.1 Positive Integers
Ms. Vallejo gave each student money from winning the lottery and asked them to make the greatest value using only 4 numbers. The document then covered exponents and exponential growth, including definitions of exponential growth and examples of multiplying exponents.
Alg1 7.8 Point-Slope Form
This document summarizes lesson 7.8 on point-slope form in algebra 1. It discusses the standard form, slope-intercept form, and point-slope form of a line, and how to write the equation of a line in point-slope form given a point and slope. It also shows how to work backwards by being given the point-slope form to find the slope and point. Students are given examples of using point-slope form and working backwards, and practice problems to complete on their own.
4.14 equations with fractions and mixed numbers
This pre-algebra lesson reviews key concepts for working with fractions and mixed numbers in equations, including:
- Inverse operations for solving equations
- Adding, subtracting, multiplying, and dividing mixed numbers
- Examples of equations with fractions and mixed numbers that must be solved using the appropriate operations.
Pre-Alg 5.5 Equations with Mixed Operations
This document discusses solving equations with mixed operations. It explains that the order of operations is SADMEP (Subtraction, Addition, Division, Multiplication, Exponents, Parentheses) and provides examples of solving equations step-by-step by combining like terms, moving terms to one side of the equation using inverse operations, and simplifying. The document provides examples of solving equations with variables like x, n, and examples of solving equations with mixed addition, subtraction, multiplication, and division terms.
Alg1 7.7 Slope-Intercept Form
This document discusses slope-intercept form for graphing lines. It defines slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. The document provides examples of graphing lines from their equations in slope-intercept form. It also shows how to convert between standard form and slope-intercept form.
Alg1 7.5 Slope
This document provides a lesson on slope in Algebra 1. It reviews ordered pairs and the x-axis and y-axis. It defines slope as the steepness of a line, or the vertical change over the horizontal change. Positive slope lines slant up, negative slope lines slant down, and zero slope lines are horizontal. The slope formula is defined as the rise over the run, or (y2-y1) over (x2-x1). Examples are given to find the slopes of lines between two points using the formula.
Pre-Alg 3.1 Multiplying Integers & Decimals
The document discusses multiplication and division of integers and decimals. It provides rules for multiplying and dividing integers, such as two positives or a positive and a negative multiplying to be positive or negative. It also discusses how the Babylonians developed multiplication as repeated addition and division as repeated subtraction over 4000 years ago. Examples are provided to demonstrate multiplying and dividing integers and decimals according to order of operations.
Alg1 4.12 Solving Equations Review
This document provides a review of solving equations. It begins with an overview of the order of operations using PEMDAS/PEDMAS. It then contrasts the difference between expressions and equations, explaining that expressions are simplified while equations are solved. The document outlines the steps to solve for a variable in an equation: simplify, combine like terms, isolate the term with the variable, and then isolate the variable. Examples are provided to illustrate these steps.
Pre-Alg 2.15 Adding & Subtracting Equations
This document is a lesson on addition and subtraction applications in pre-algebra. It discusses why word problems are important to practice and provides examples of word problems involving unit rates and multi-step word problems. It also outlines the steps to solve word problems which are to draw or write the information, form an equation, solve the equation, and check the solution.
Alg1 4.2 Multiplication & Division Equations
This document contains lessons on multiplication and division equations, inverse operations, and absolute value. It reviews solving equations, word problems, and the process of drawing, writing, forming, solving, and checking problems. Key topics covered include inverse operations, absolute value, solving equations with variables on both sides, and using a multi-step process to solve word problems.
Pre-Algebra 2.11 2.12 Subtracting Decimals
This document provides an overview of subtracting decimals including:
1) Rules for subtracting decimals based on sign including same sign add and different signs take the difference and keep the sign of the higher number
2) Examples of how any subtraction problem can be turned into an addition problem by changing the operation sign
3) A set of practice problems subtracting decimals
Alg 1 3.6 Reciprocals and Division
The document discusses reciprocals and division in algebra 1. It explains that finding the reciprocal of a number or fraction involves flipping the numerator and denominator. Several examples are provided of converting decimals to fractions and finding their reciprocals. Key properties of reciprocals are defined, such as the reciprocal of a product equals the product of the reciprocals. The document emphasizes that division can be represented as multiplying by a reciprocal. Practice problems are included for students to work through.
Algebra 1 2.8 Algebraic Proof
This document contains an algebra 1 lesson on algebraic proofs. It provides examples of algebraic proofs for equations such as 9=5+4, -5=3x+1, and 2x-30=-4x+6. Each proof is shown step-by-step including the statement and reason for each step using properties of equality, addition, subtraction, multiplication, and division. The document also defines and provides examples of algebraic properties used in proofs such as the commutative, associative, and distributive properties.
Pre-Algebra 2.8 Adding Decimals
The document provides an overview of lessons on adding decimals from Pre-Algebra Unit 2. It defines decimals, reviews the rules for adding decimals depending on the signs, and provides examples. It then describes activities for students to practice adding decimals using their own birthdays and comparing decimal expressions and inverse operations.
More from Jaqueline Vallejo (20)
Input output tables
- 3. Functions in real life
- 5. Example of a function: y=x+3 y=x+3 y=x+3 x y 1 5 y=x+3 7 fill out table
- 6. Your turn: y=x-4 x y 12 14 15
- 7. Your turn: y = -3x x y 1 2 3
- 8. What about this one: y = 2x + 3 x y 1 2 3
- 9. x A little more difficult: y= -3 2 x y 6 10 14
- 11. Can you do it backwards?
- 12. I'll give you the table, you find the function x y x y 5 1 2 100 7 3 3 150 10 6 4 200